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Solving Absolute Value Inequalities

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Presentation on theme: "Solving Absolute Value Inequalities"β€” Presentation transcript:

1 Solving Absolute Value Inequalities
Algebra 2 Unit 1, Lesson 2.3

2 Solving Absolute Value Inequalities
Algebraically Graphically

3 Solve Algebraically

4 Solve Algebraically 4βˆ’π‘₯ +15>21

5 Solve on your own: π‘₯+1 βˆ’10β‰€βˆ’2
Remember to isolate absolute value Separate into two equations and reverse.

6 Solution 4βˆ’π‘₯ +15β‰₯21 βˆ’12≀π‘₯ π‘Žπ‘›π‘‘ π‘₯≀4 βˆ’12≀π‘₯≀4
βˆ’12≀π‘₯ π‘Žπ‘›π‘‘ π‘₯≀ βˆ’12≀π‘₯≀4 Why is the format of the solution different?

7 Practice Pause and solve problems 11, 12, and 13 from lesson 3 in your assignment packet. 11. 2 π‘₯βˆ’ >4 π‘₯+1 βˆ’4<5 π‘₯+4 +2β‰₯5

8 Practice Solutions 11. π‘₯<3 π‘œπ‘Ÿ π‘₯>4
12. βˆ’5<π‘₯ π‘Žπ‘›π‘‘ π‘₯< βˆ’5<π‘₯<4 13. π‘₯β‰€βˆ’5 π‘œπ‘Ÿ π‘₯β‰₯βˆ’3 π‘₯<3 π‘œπ‘Ÿ π‘₯>4

9 Solving Graphically π‘₯+3 +1>4
Solve the inequality graphically Graph both sides of the equation y= π‘₯+3 +1 𝑦=4

10 Solving Graphically π‘₯+3 +1>4
Solve the inequality graphically Graph both sides of the equation y= π‘₯+3 +1 𝑦=4 Intervals on the x axis: βˆ’6β‰₯π‘₯ π‘œπ‘Ÿ π‘₯β‰₯0

11 On your Own Solve: π‘₯ βˆ’2 βˆ’3≀1 Hint: Begin by graphing both sides

12 On your Own Solve: π‘₯ βˆ’2 βˆ’3≀1 Final Solution βˆ’2≀π‘₯≀6
Hint: Begin by graphing both sides Final Solution βˆ’2≀π‘₯≀6 Why different format?

13 Final Thoughts When does an absolute value inequality apply to a real-world situation? Remember you can always check your solution but placing a value in for the variable to see if the equation remains true.


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